Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

sample32.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5321	37

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 25.2b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
24.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
6×	`associate-*r/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 97

Calls

4 calls:

12.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
10.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
7.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
29.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series58.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
35.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify50.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	2437
1	4994	2437

prune246.0ms

Filtered

78 candidates to 109 candidates (-39.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 0.0b

Counts

111 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
7.2b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
16.2b	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
21.2b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
44.0ms	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
30.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
8.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
36.0ms	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
54.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify148.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5067	17965

prune867.0ms

Filtered

143 candidates to 276 candidates (-93.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	275	7	282

Merged error: 0.0b

Counts

282 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.5b	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
24.6b	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`add-exp-log` `associate-r`
20×	`times-frac`
15×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
6×	`flip3-+` `prod-exp` `flip-+`
5×	`associate-*r/` `unswap-sqr`
4×	`div-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `rec-exp` `distribute-lft-in` `1-exp` `associate-*l/` `div-inv`
1×	`pow-flip` `frac-2neg` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 119

Calls

4 calls:

10.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
7.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
14.0ms	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
30.0ms	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
6.0ms	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
39.0ms	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5547	2985

prune244.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Merged error: 0.0b

Counts

138 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
15.3b	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
15.3b	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
16.2b	(/ (* (* (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
26×	`sqrt-prod`
24×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
11×	`associate-/l/`
10×	`cbrt-div` `sqrt-div` `prod-exp` `cbrt-unprod`
9×	`frac-times` `associate-*l/`
8×	`pow1` `sqrt-pow1` `flip3-+` `flip-+`
6×	`times-frac` `associate-/r*`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
3×	`cbrt-prod` `associate-*r/`
2×	`associate-/r/`
1×	`frac-2neg` `pow1/3` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
13.0ms	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
15.0ms	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
89.0ms	(/ (* (* (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
12.0ms	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
10.0ms	(sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
40.0ms	(/ (* (* (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (/ (cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4980	4483
1	4980	4483

prune590.0ms

Filtered

80 candidates to 117 candidates (-46.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	117	7	124

Merged error: 0.0b

Counts

124 → 7

regimes368.0ms

Accuracy

97.2% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 25.3b

bsearch46.0ms

Steps

Iters	Range		Point
10	1.0740801789565234e+49	2.769656315482433e+62	1.2853152778572147e+52
7	-1.1516932916285229e+44	-4.252965012697481e+42	-4.3089601253124313e+43

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	79
1	91	79

end0.0ms

sample801.0ms

Algorithm

intervals

Results

631.0ms	8000×	body	80	valid
1.0ms	8×	body	80	invalid

Details

analyze1.2s

sample32.0ms

simplify36.0ms

prune11.0ms

localize22.0ms

rewrite60.0ms

series58.0ms

simplify50.0ms

prune246.0ms

localize26.0ms

rewrite111.0ms

series104.0ms

simplify148.0ms

prune867.0ms

localize26.0ms

rewrite63.0ms

series55.0ms

simplify56.0ms

prune244.0ms

localize36.0ms

rewrite133.0ms

series94.0ms

simplify65.0ms

prune590.0ms

regimes368.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample801.0ms

Profiling